I don't know why I read threads like this, I just end up getting a bad case of GAS for half of everything mentioned (Motor City Big Block DI? Chase Tone Secret? How did I not know about such things?!?!?!?). Damn you @el murdoque
But also ... The Sushibox Finally is excellent in this regard. Many tube DIs fit the bill - The Noble, and I just got an SVTDi, a Khan, and a. Demeter DI (to compare) and they all add something special in different ways. The Finally stands out because it is much less $$$ but sounds incredible. The SIB Fatdrive is also one tube pre that adds a little something that I rarely hear in other tube pres.
Non-tube, the boxes that I haven't seen mentioned that come to mind are the Fre the Tone Bass Blaster and two compressors - the Cali76, which adds a nice punch and the Becos Stella, which not only adds a nice punch but also has vintage tape saturation capability, which I imagine is something like what the Emerald Prince and Chase Secret preamps also add.
Finally, for tone shaping devices, the JHS Colourbox has that Neve sound inherent in it's design. It pairs well with tube pres to really bring out a great tone.